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Verify that this function -2π 1 f(z): = 2πT o exp(2z cost) dt is entire, with the power series representation 2π f(2) = Σ n=0 () 2 for zЄ C. (Hint. You must use the power series of the exponential map. You need the value of 2 cosn t dt which can be found by repeated integration by parts.)

Verify that this function -2π 1 f(z): = 2πT o exp(2z cost) dt is entire, with the power series representation 2π f(2) = Σ n=0 () 2 for zЄ C. (Hint. You must use the power series of the exponential map. You need the value of 2 cosn t dt which can be found by repeated integration by parts.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Verify that this function -2π 1 f(z): = 2πT o exp(2z cost) dt is entire, with the power series representation 2π f(2) = Σ n=0 () 2 for zЄ C. (Hint. You must use the power series of the exponential map. You need the value of 2 cosn t dt which can be found by repeated integration by parts.)
Transcribed Image Text:Verify that this function -2π 1 f(z): = 2πT o exp(2z cost) dt is entire, with the power series representation 2π f(2) = Σ n=0 () 2 for zЄ C. (Hint. You must use the power series of the exponential map. You need the value of 2 cosn t dt which can be found by repeated integration by parts.)
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